We present PLONQ, a progressive neural image compression scheme which pushes the boundary of variable bitrate compression by allowing quality scalable coding with a single bitstream. In contrast to existing learned variable bitrate solutions which produce separate bitstreams for each quality, it enables easier rate-control and requires less storage. Leveraging the latent scaling based variable bitrate solution, we introduce nested quantization, a method that defines multiple quantization levels with nested quantization grids, and progressively refines all latents from the coarsest to the finest quantization level. To achieve finer progressiveness in between any two quantization levels, latent elements are incrementally refined with an importance ordering defined in the rate-distortion sense. To the best of our knowledge, PLONQ is the first learning-based progressive image coding scheme and it outperforms SPIHT, a well-known wavelet-based progressive image codec.